Known large-angle constant-speed joints designed for driving the driving and steering wheels of front-wheel drive automobile vehicles, usually comprise rolling elements which transfer the driving forces by pressure exerted by their surfaces on tracks. This pressure of contact, termed "Hertz", becomes very high principally when these joints operate at a large angle, since the direction of the pressing forces is off centre relative to the plane of symmetry of the tracks. Thus, the pressure of contact produces under the pressed surface shear stresses which exceed the strength of the treated steels so that the allowable torque at the maximum angle of operation is limited. The possibility of a high torque at an operating angle is required, in particular in the case of a critical starting, for example for getting a vehicle out of a bogged situation with the steering turned through the full lock.